Imports

In [1]:
import pandas as pd
import seaborn as sns
import matplotlib.pyplot as plt
from sklearn.preprocessing import StandardScaler,LabelEncoder
import numpy as np
from sklearn.cluster import KMeans
from sklearn.model_selection import GridSearchCV
# %matplotlib inline
In [2]:
data = pd.read_csv('Data for Associate DS.csv',)
data.head()
Out[2]:
CUST_ID BALANCE BALANCE_FREQUENCY PURCHASES ONEOFF_PURCHASES INSTALLMENTS_PURCHASES CASH_ADVANCE PURCHASES_FREQUENCY ONEOFF_PURCHASES_FREQUENCY PURCHASES_INSTALLMENTS_FREQUENCY CASH_ADVANCE_FREQUENCY CASH_ADVANCE_TRX PURCHASES_TRX CREDIT_LIMIT PAYMENTS MINIMUM_PAYMENTS PRC_FULL_PAYMENT TENURE
0 C10001 40.900749 0.818182 95.40 0.00 95.4 0.000000 0.166667 0.000000 0.083333 0.000000 0 2 1000.0 201.802084 139.509787 0.000000 12
1 C10002 3202.467416 0.909091 0.00 0.00 0.0 6442.945483 0.000000 0.000000 0.000000 0.250000 4 0 7000.0 4103.032597 1072.340217 0.222222 12
2 C10003 2495.148862 1.000000 773.17 773.17 0.0 0.000000 1.000000 1.000000 0.000000 0.000000 0 12 7500.0 622.066742 627.284787 0.000000 12
3 C10004 1666.670542 0.636364 1499.00 1499.00 0.0 205.788017 0.083333 0.083333 0.000000 0.083333 1 1 7500.0 0.000000 NaN 0.000000 12
4 C10005 817.714335 1.000000 16.00 16.00 0.0 0.000000 0.083333 0.083333 0.000000 0.000000 0 1 1200.0 678.334763 244.791237 0.000000 12
In [3]:
data.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 8950 entries, 0 to 8949
Data columns (total 18 columns):
 #   Column                            Non-Null Count  Dtype  
---  ------                            --------------  -----  
 0   CUST_ID                           8950 non-null   object 
 1   BALANCE                           8950 non-null   float64
 2   BALANCE_FREQUENCY                 8950 non-null   float64
 3   PURCHASES                         8950 non-null   float64
 4   ONEOFF_PURCHASES                  8950 non-null   float64
 5   INSTALLMENTS_PURCHASES            8950 non-null   float64
 6   CASH_ADVANCE                      8950 non-null   float64
 7   PURCHASES_FREQUENCY               8950 non-null   float64
 8   ONEOFF_PURCHASES_FREQUENCY        8950 non-null   float64
 9   PURCHASES_INSTALLMENTS_FREQUENCY  8950 non-null   float64
 10  CASH_ADVANCE_FREQUENCY            8950 non-null   float64
 11  CASH_ADVANCE_TRX                  8950 non-null   int64  
 12  PURCHASES_TRX                     8950 non-null   int64  
 13  CREDIT_LIMIT                      8949 non-null   float64
 14  PAYMENTS                          8950 non-null   float64
 15  MINIMUM_PAYMENTS                  8637 non-null   float64
 16  PRC_FULL_PAYMENT                  8950 non-null   float64
 17  TENURE                            8950 non-null   int64  
dtypes: float64(14), int64(3), object(1)
memory usage: 1.2+ MB
In [4]:
data.describe()
Out[4]:
BALANCE BALANCE_FREQUENCY PURCHASES ONEOFF_PURCHASES INSTALLMENTS_PURCHASES CASH_ADVANCE PURCHASES_FREQUENCY ONEOFF_PURCHASES_FREQUENCY PURCHASES_INSTALLMENTS_FREQUENCY CASH_ADVANCE_FREQUENCY CASH_ADVANCE_TRX PURCHASES_TRX CREDIT_LIMIT PAYMENTS MINIMUM_PAYMENTS PRC_FULL_PAYMENT TENURE
count 8950.000000 8950.000000 8950.000000 8950.000000 8950.000000 8950.000000 8950.000000 8950.000000 8950.000000 8950.000000 8950.000000 8950.000000 8949.000000 8950.000000 8637.000000 8950.000000 8950.000000
mean 1564.474828 0.877271 1003.204834 592.437371 411.067645 978.871112 0.490351 0.202458 0.364437 0.135144 3.248827 14.709832 4494.449450 1733.143852 864.206542 0.153715 11.517318
std 2081.531879 0.236904 2136.634782 1659.887917 904.338115 2097.163877 0.401371 0.298336 0.397448 0.200121 6.824647 24.857649 3638.815725 2895.063757 2372.446607 0.292499 1.338331
min 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 50.000000 0.000000 0.019163 0.000000 6.000000
25% 128.281915 0.888889 39.635000 0.000000 0.000000 0.000000 0.083333 0.000000 0.000000 0.000000 0.000000 1.000000 1600.000000 383.276166 169.123707 0.000000 12.000000
50% 873.385231 1.000000 361.280000 38.000000 89.000000 0.000000 0.500000 0.083333 0.166667 0.000000 0.000000 7.000000 3000.000000 856.901546 312.343947 0.000000 12.000000
75% 2054.140036 1.000000 1110.130000 577.405000 468.637500 1113.821139 0.916667 0.300000 0.750000 0.222222 4.000000 17.000000 6500.000000 1901.134317 825.485459 0.142857 12.000000
max 19043.138560 1.000000 49039.570000 40761.250000 22500.000000 47137.211760 1.000000 1.000000 1.000000 1.500000 123.000000 358.000000 30000.000000 50721.483360 76406.207520 1.000000 12.000000
In [5]:
#finding if there is any missing value

data.isnull().sum()
Out[5]:
CUST_ID                               0
BALANCE                               0
BALANCE_FREQUENCY                     0
PURCHASES                             0
ONEOFF_PURCHASES                      0
INSTALLMENTS_PURCHASES                0
CASH_ADVANCE                          0
PURCHASES_FREQUENCY                   0
ONEOFF_PURCHASES_FREQUENCY            0
PURCHASES_INSTALLMENTS_FREQUENCY      0
CASH_ADVANCE_FREQUENCY                0
CASH_ADVANCE_TRX                      0
PURCHASES_TRX                         0
CREDIT_LIMIT                          1
PAYMENTS                              0
MINIMUM_PAYMENTS                    313
PRC_FULL_PAYMENT                      0
TENURE                                0
dtype: int64
In [6]:
data.nunique()
Out[6]:
CUST_ID                             8950
BALANCE                             8871
BALANCE_FREQUENCY                     43
PURCHASES                           6203
ONEOFF_PURCHASES                    4014
INSTALLMENTS_PURCHASES              4452
CASH_ADVANCE                        4323
PURCHASES_FREQUENCY                   47
ONEOFF_PURCHASES_FREQUENCY            47
PURCHASES_INSTALLMENTS_FREQUENCY      47
CASH_ADVANCE_FREQUENCY                54
CASH_ADVANCE_TRX                      65
PURCHASES_TRX                        173
CREDIT_LIMIT                         205
PAYMENTS                            8711
MINIMUM_PAYMENTS                    8636
PRC_FULL_PAYMENT                      47
TENURE                                 7
dtype: int64
In [7]:
#imputing the missing values with median

data.CREDIT_LIMIT.fillna(data.CREDIT_LIMIT.median(),inplace = True)

data.MINIMUM_PAYMENTS.fillna(data.MINIMUM_PAYMENTS.median(),inplace = True)
In [8]:
data.isna().sum()
Out[8]:
CUST_ID                             0
BALANCE                             0
BALANCE_FREQUENCY                   0
PURCHASES                           0
ONEOFF_PURCHASES                    0
INSTALLMENTS_PURCHASES              0
CASH_ADVANCE                        0
PURCHASES_FREQUENCY                 0
ONEOFF_PURCHASES_FREQUENCY          0
PURCHASES_INSTALLMENTS_FREQUENCY    0
CASH_ADVANCE_FREQUENCY              0
CASH_ADVANCE_TRX                    0
PURCHASES_TRX                       0
CREDIT_LIMIT                        0
PAYMENTS                            0
MINIMUM_PAYMENTS                    0
PRC_FULL_PAYMENT                    0
TENURE                              0
dtype: int64

Deriving new Key Performance Indicators for by implementing Feature Engineering:

1. Monthly average purchase and advance amount.

In [9]:
#The average monthly purchase will be the total purchases

data['Monthly_avg_purchase'] = data['PURCHASES'] / data['TENURE']
In [10]:
# different tenure values of different customers

print(data.groupby('TENURE')['TENURE'].count())

TENURE
6      204
7      190
8      196
9      175
10     236
11     365
12    7584
Name: TENURE, dtype: int64

Advance amount:

In [11]:
data['Monthly_cash_advance'] = data['CASH_ADVANCE'] / data['TENURE']

Types of purchases (one-off or installments):

In [12]:
data.loc[:,['ONEOFF_PURCHASES','INSTALLMENTS_PURCHASES']]
Out[12]:
ONEOFF_PURCHASES INSTALLMENTS_PURCHASES
0 0.00 95.40
1 0.00 0.00
2 773.17 0.00
3 1499.00 0.00
4 16.00 0.00
... ... ...
8945 0.00 291.12
8946 0.00 300.00
8947 0.00 144.40
8948 0.00 0.00
8949 1093.25 0.00

8950 rows × 2 columns

In [13]:
plt.figure(figsize = (8,7))
sns.set_style('darkgrid')
ax = sns.scatterplot(data = data,y = data.ONEOFF_PURCHASES,x = data.INSTALLMENTS_PURCHASES,marker = '.',s = (200,200))
plt.show()

2. Types of purchases(one-off,installments):

In [14]:
def purchase_type(data):
    if(data['ONEOFF_PURCHASES'] == 0) & (data['INSTALLMENTS_PURCHASES'] == 0):
        return 'No Purchase'
    if(data['ONEOFF_PURCHASES'] > 0) & (data['INSTALLMENTS_PURCHASES'] == 0):
        return 'One Off Purchase'
    if(data['ONEOFF_PURCHASES'] == 0) & (data['INSTALLMENTS_PURCHASES'] > 0):
        return 'Installment '
    if(data['ONEOFF_PURCHASES'] > 0) & (data['INSTALLMENTS_PURCHASES'] > 0):
         return 'Both'
In [15]:
data['Purchase_Type'] = data.apply(purchase_type,axis = 1)
In [16]:
# We can know the different types of categories of customer by looking at the type of purchases
data['Purchase_Type'].value_counts()
Out[16]:
Both                2774
Installment         2260
No Purchase         2042
One Off Purchase    1874
Name: Purchase_Type, dtype: int64
In [17]:
sns.countplot(data = data,x = 'Purchase_Type')
plt.title('Count of distinct purchase types')
plt.show()

It is visible that most people did both type of purchases.

4. Limit Usage (balance to credit limit ratio)

In [18]:
data['Limit Usage'] = data['BALANCE'] / data['CREDIT_LIMIT']
In [19]:
# data['Limit Usage'] = data['Limit Usage'] / 100
data['Limit Usage']
Out[19]:
0       0.040901
1       0.457495
2       0.332687
3       0.222223
4       0.681429
          ...   
8945    0.028494
8946    0.019183
8947    0.023399
8948    0.026915
8949    0.310590
Name: Limit Usage, Length: 8950, dtype: float64
In [20]:
sns.lineplot(data = data,y = data['Limit Usage'] * 100,x = 'CREDIT_LIMIT',)
plt.ylabel('Limit Usage in %')
plt.ylim(0, 200)
plt.show()
In [21]:
## Number of people who spend more than their credit limit:

data[data['Limit Usage'] > 1].shape[0]
Out[21]:
227

Conclusion:

There are 227 people who overspend.

5. Payments to minimum payments ratio.

In [22]:
data['Pay_To_Min_Pay_Ratio'] = data['PAYMENTS'] / data['MINIMUM_PAYMENTS']
In [23]:
data.Pay_To_Min_Pay_Ratio
Out[23]:
0       1.446508
1       3.826241
2       0.991682
3       0.000000
4       2.771075
          ...   
8945    6.660231
8946    0.883197
8947    0.986076
8948    0.942505
8949    0.715439
Name: Pay_To_Min_Pay_Ratio, Length: 8950, dtype: float64
In [24]:
data['Purchase_Type'].describe()
Out[24]:
count     8950
unique       4
top       Both
freq      2774
Name: Purchase_Type, dtype: object

6. Based on purchase frequency, we can create a new KPI: Purchase Frequency Class(<=25%, >25 and <= 50 etc..)

In [25]:
def purchase_class(data):
    if(data['PURCHASES_FREQUENCY'] * 100 < 25):
        return '0 to 24'
    if(data['PURCHASES_FREQUENCY'] * 100 < 50):
        return '25 to 49'
    if(data['PURCHASES_FREQUENCY'] * 100 < 75):
        return '50 to 74'
    return '75 to 100'
In [26]:
data['PURCHASES_FREQUENCY_CLASS'] = data.apply(purchase_class,axis = 1)
data.PURCHASES_FREQUENCY_CLASS.value_counts()
Out[26]:
75 to 100    3403
0 to 24      3305
50 to 74     1139
25 to 49     1103
Name: PURCHASES_FREQUENCY_CLASS, dtype: int64
In [27]:
#plotting the purchase frequency class KPI:

sns.countplot(data = data,x = 'PURCHASES_FREQUENCY_CLASS')
plt.title('Count of different purchases frequency percentages:')
plt.show()

We can observe that most of the customers lie between either less than 25 or greater than 75 percent.

In [28]:
data.describe()
Out[28]:
BALANCE BALANCE_FREQUENCY PURCHASES ONEOFF_PURCHASES INSTALLMENTS_PURCHASES CASH_ADVANCE PURCHASES_FREQUENCY ONEOFF_PURCHASES_FREQUENCY PURCHASES_INSTALLMENTS_FREQUENCY CASH_ADVANCE_FREQUENCY ... PURCHASES_TRX CREDIT_LIMIT PAYMENTS MINIMUM_PAYMENTS PRC_FULL_PAYMENT TENURE Monthly_avg_purchase Monthly_cash_advance Limit Usage Pay_To_Min_Pay_Ratio
count 8950.000000 8950.000000 8950.000000 8950.000000 8950.000000 8950.000000 8950.000000 8950.000000 8950.000000 8950.000000 ... 8950.000000 8950.000000 8950.000000 8950.000000 8950.000000 8950.000000 8950.000000 8950.000000 8950.000000 8950.000000
mean 1564.474828 0.877271 1003.204834 592.437371 411.067645 978.871112 0.490351 0.202458 0.364437 0.135144 ... 14.709832 4494.282473 1733.143852 844.906767 0.153715 11.517318 86.175173 88.977984 0.388884 9.059164
std 2081.531879 0.236904 2136.634782 1659.887917 904.338115 2097.163877 0.401371 0.298336 0.397448 0.200121 ... 24.857649 3638.646702 2895.063757 2332.792322 0.292499 1.338331 180.508787 193.136115 0.389722 118.180526
min 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 ... 0.000000 50.000000 0.000000 0.019163 0.000000 6.000000 0.000000 0.000000 0.000000 0.000000
25% 128.281915 0.888889 39.635000 0.000000 0.000000 0.000000 0.083333 0.000000 0.000000 0.000000 ... 1.000000 1600.000000 383.276166 170.857654 0.000000 12.000000 3.399375 0.000000 0.041494 0.913275
50% 873.385231 1.000000 361.280000 38.000000 89.000000 0.000000 0.500000 0.083333 0.166667 0.000000 ... 7.000000 3000.000000 856.901546 312.343947 0.000000 12.000000 31.936667 0.000000 0.302720 2.032717
75% 2054.140036 1.000000 1110.130000 577.405000 468.637500 1113.821139 0.916667 0.300000 0.750000 0.222222 ... 17.000000 6500.000000 1901.134317 788.713501 0.142857 12.000000 97.228333 99.085196 0.717571 6.052729
max 19043.138560 1.000000 49039.570000 40761.250000 22500.000000 47137.211760 1.000000 1.000000 1.000000 1.500000 ... 358.000000 30000.000000 50721.483360 76406.207520 1.000000 12.000000 4086.630833 3928.100980 15.909951 6840.528861

8 rows × 21 columns

Preprocessing the data

In [29]:
# dropping the cutomer id column
data.drop(['CUST_ID'],axis = 1,inplace=True)
data.columns
Out[29]:
Index(['BALANCE', 'BALANCE_FREQUENCY', 'PURCHASES', 'ONEOFF_PURCHASES',
       'INSTALLMENTS_PURCHASES', 'CASH_ADVANCE', 'PURCHASES_FREQUENCY',
       'ONEOFF_PURCHASES_FREQUENCY', 'PURCHASES_INSTALLMENTS_FREQUENCY',
       'CASH_ADVANCE_FREQUENCY', 'CASH_ADVANCE_TRX', 'PURCHASES_TRX',
       'CREDIT_LIMIT', 'PAYMENTS', 'MINIMUM_PAYMENTS', 'PRC_FULL_PAYMENT',
       'TENURE', 'Monthly_avg_purchase', 'Monthly_cash_advance',
       'Purchase_Type', 'Limit Usage', 'Pay_To_Min_Pay_Ratio',
       'PURCHASES_FREQUENCY_CLASS'],
      dtype='object')
In [30]:
cont_features = []
for i in data.columns:
    if((data[i].dtype) == 'int64' or (data[i].dtype) == 'float64'):
        cont_features.append(i)

cont_features
Out[30]:
['BALANCE',
 'BALANCE_FREQUENCY',
 'PURCHASES',
 'ONEOFF_PURCHASES',
 'INSTALLMENTS_PURCHASES',
 'CASH_ADVANCE',
 'PURCHASES_FREQUENCY',
 'ONEOFF_PURCHASES_FREQUENCY',
 'PURCHASES_INSTALLMENTS_FREQUENCY',
 'CASH_ADVANCE_FREQUENCY',
 'CASH_ADVANCE_TRX',
 'PURCHASES_TRX',
 'CREDIT_LIMIT',
 'PAYMENTS',
 'MINIMUM_PAYMENTS',
 'PRC_FULL_PAYMENT',
 'TENURE',
 'Monthly_avg_purchase',
 'Monthly_cash_advance',
 'Limit Usage',
 'Pay_To_Min_Pay_Ratio']
In [31]:
# standardizing the columns with mean > 0 or std > 1
sc = StandardScaler()
for i in cont_features:
    data[i] = sc.fit_transform(data[i].values.reshape(-1,1))
In [32]:
data.head()
Out[32]:
BALANCE BALANCE_FREQUENCY PURCHASES ONEOFF_PURCHASES INSTALLMENTS_PURCHASES CASH_ADVANCE PURCHASES_FREQUENCY ONEOFF_PURCHASES_FREQUENCY PURCHASES_INSTALLMENTS_FREQUENCY CASH_ADVANCE_FREQUENCY ... PAYMENTS MINIMUM_PAYMENTS PRC_FULL_PAYMENT TENURE Monthly_avg_purchase Monthly_cash_advance Purchase_Type Limit Usage Pay_To_Min_Pay_Ratio PURCHASES_FREQUENCY_CLASS
0 -0.731989 -0.249434 -0.424900 -0.356934 -0.349079 -0.466786 -0.806490 -0.678661 -0.707313 -0.675349 ... -0.528979 -0.302400 -0.525551 0.36068 -0.433384 -0.460727 Installment -0.892951 -0.064419 0 to 24
1 0.786961 0.134325 -0.469552 -0.356934 -0.454576 2.605605 -1.221758 -0.678661 -0.916995 0.573963 ... 0.818642 0.097500 0.234227 0.36068 -0.477428 2.319396 No Purchase 0.176063 -0.044282 0 to 24
2 0.447135 0.518084 -0.107668 0.108889 -0.454576 -0.466786 1.269843 2.673451 -0.916995 -0.675349 ... -0.383805 -0.093293 -0.525551 0.36068 -0.120468 -0.460727 One Off Purchase -0.144206 -0.068268 75 to 100
3 0.049099 -1.016953 0.232058 0.546189 -0.454576 -0.368653 -1.014125 -0.399319 -0.916995 -0.258913 ... -0.598688 -0.228307 -0.525551 0.36068 0.214636 -0.371929 One Off Purchase -0.427665 -0.076660 0 to 24
4 -0.358775 0.518084 -0.462063 -0.347294 -0.454576 -0.466786 -1.014125 -0.399319 -0.916995 -0.675349 ... -0.364368 -0.257266 -0.525551 0.36068 -0.470041 -0.460727 One Off Purchase 0.750693 -0.053210 0 to 24

5 rows × 23 columns

In [33]:
# encoding categorical variables

cat_features = []
for i in data.columns:
    if((data[i].dtype) == 'object'):
        cat_features.append(i)

cat_features
Out[33]:
['Purchase_Type', 'PURCHASES_FREQUENCY_CLASS']
In [34]:
label_encoder = LabelEncoder()
for i in cat_features:
    data[i] = label_encoder.fit_transform(data[i].values.reshape(-1,1))
In [35]:
data[cat_features].nunique()
Out[35]:
Purchase_Type                4
PURCHASES_FREQUENCY_CLASS    4
dtype: int64

Now that our data is ready, we can apply PCA for dimensionality reduction.

In [36]:
sns.heatmap(data.corr())
plt.show()
In [37]:
covariance_matrix = np.cov(data.T)
covariance_matrix[0:3]
Out[37]:
array([[ 1.00011174,  0.32244833,  0.181281  ,  0.16436802,  0.12648316,
         0.49674704, -0.07795245,  0.07317426, -0.06319282,  0.44926823,
         0.38519531,  0.15435561,  0.53135553,  0.32283773,  0.39796451,
        -0.31899484,  0.07270039,  0.17973145,  0.47548389,  0.00268393,
         0.50361295, -0.03945057, -0.09514337],
       [ 0.32244833,  1.00011174,  0.13368937,  0.10433488,  0.12430607,
         0.0993991 ,  0.22974114,  0.20243794,  0.17609907,  0.19189412,
         0.14157068,  0.18964713,  0.095942  ,  0.06501513,  0.13119544,
        -0.09509307,  0.11978927,  0.13129551,  0.08602949, -0.15716001,
         0.40470617, -0.08928162,  0.3131779 ],
       [ 0.181281  ,  0.13368937,  1.00011174,  0.91694701,  0.67997219,
        -0.05147997,  0.39306135,  0.49848543,  0.31560195, -0.12015662,
        -0.06718279,  0.68963789,  0.35701681,  0.60333124,  0.09579955,
         0.18039922,  0.08629784,  0.99595653, -0.0554787 , -0.33304885,
        -0.05741503,  0.01673261,  0.50150695]])
In [38]:
eigen_values,eigen_vectors = np.linalg.eig(covariance_matrix)
eigen_vectors[0:3]
Out[38]:
array([[ 6.10584221e-03,  3.61287764e-01, -1.02466148e-01,
        -2.37636612e-01,  1.59535169e-01,  1.29118696e-01,
         2.35522267e-03, -2.45422225e-01,  1.66788817e-01,
         1.87718109e-01,  3.56393659e-02,  7.18765927e-02,
         8.08797543e-02, -3.59062043e-01,  1.43890990e-01,
         4.37554975e-02, -5.21624677e-01,  4.46314234e-01,
        -2.75103743e-02, -2.17761846e-02, -1.88526933e-03,
         3.81090951e-04, -4.09999943e-05],
       [ 7.99645681e-02,  1.37999306e-01, -2.33006900e-01,
        -3.52523590e-01, -3.10054946e-01,  1.63332454e-01,
        -6.45324273e-02,  1.45776341e-01, -2.54566765e-01,
         5.27968396e-01, -1.29539198e-01,  2.81275080e-02,
        -2.29671520e-01,  4.69472058e-01,  5.36149638e-02,
        -8.06508501e-02, -1.38486695e-02,  6.25596418e-02,
        -7.14211944e-04, -2.24543497e-03, -5.91522363e-04,
         2.44989928e-04, -9.97621577e-06],
       [ 2.97523312e-01,  1.63077419e-01,  3.02243668e-01,
        -5.21668976e-02, -3.77496555e-02, -1.52504298e-01,
         2.14593895e-02,  8.62478787e-02,  1.01671509e-02,
         1.00579496e-02,  6.58669318e-03,  4.78198653e-02,
        -1.27233992e-01, -2.08347972e-02,  4.61561789e-02,
         1.99541764e-01,  1.54753729e-02, -1.47120270e-02,
        -6.85799085e-03,  2.45202832e-02, -2.23242146e-03,
        -3.66230337e-01,  7.49595105e-01]])
In [39]:
eigen_vec_svd,s , v = np.linalg.svd(data.T)
eigen_vec_svd[0:3]
Out[39]:
array([[-2.94704606e-04,  2.58358595e-01, -2.54075145e-01,
        -9.93789384e-02,  2.37558046e-01, -2.12152586e-01,
        -2.06493126e-02, -3.61886800e-02,  2.72268548e-01,
        -8.41603654e-02, -1.88723714e-01, -3.86990112e-02,
         1.19302616e-01, -3.46599163e-01,  1.47289044e-01,
        -3.70056065e-02,  2.74003196e-01, -6.27037213e-01,
         1.04575772e-01,  1.48731452e-02,  2.18181833e-02,
         3.55754593e-04, -4.00091390e-05],
       [ 7.70622044e-02,  9.88758718e-02, -1.03849234e-01,
        -2.27283514e-01,  3.53234388e-01,  2.05517257e-01,
        -2.87431661e-01,  1.25912604e-01, -1.12403152e-01,
         3.40778005e-01, -4.84632902e-01,  1.31810846e-01,
         2.42208379e-03,  5.09367485e-01,  5.02951564e-02,
         7.41652627e-02,  8.32356004e-03, -2.73365135e-02,
         8.27839827e-02,  1.36590768e-02,  2.20989172e-03,
         1.86154770e-04, -7.38384420e-06],
       [ 2.77313562e-01,  2.03494812e-01, -2.45625793e-02,
         2.95530898e-01,  5.21635899e-02,  1.11083041e-01,
         1.01694832e-01, -1.61173786e-02, -9.05826667e-02,
        -3.58806447e-02, -1.67701774e-02, -8.05001827e-03,
         1.31494121e-01,  4.46635684e-02,  4.64568494e-02,
        -1.98032594e-01, -1.50957437e-02,  8.57740136e-03,
        -2.57117511e-02,  6.48682224e-04, -2.42999885e-02,
        -3.66255927e-01,  7.49591154e-01]])
In [40]:
for val in eigen_values:
    print(val)

6.868735824765016
4.4510868066595375
2.3419340750262547
1.73135953212714
1.1422675286572737
1.0892085568590586
0.9819211662269598
0.8962383960315053
0.7766824550320065
0.6752335528253195
0.616439932424875
0.5455117885147677
0.44845869050817855
0.41188183144764745
0.3022953833706421
0.271015504651207
0.17932513798614771
0.1737411588962744
0.07490473956746797
0.016238791383614986
0.014524824027682537
0.004405041818071403
1.1635427899263022e-05
In [41]:
var_explained = [(i/sum(eigen_values)) * 100 for i in eigen_values]
var_explained
Out[41]:
[28.60373554190112,
 18.535828592023364,
 9.752604358009286,
 7.209965770754997,
 4.7567877323235646,
 4.535832255775848,
 4.089051330302392,
 3.732239340193264,
 3.2343680279085483,
 2.8119005398922163,
 2.567064049977747,
 2.271695306348416,
 1.8675334314814853,
 1.715215038372137,
 1.2588600613079004,
 1.1286000831256602,
 0.7467704325557134,
 0.7235168579194073,
 0.31192863084032335,
 0.06762381115056439,
 0.06048627227481058,
 0.018344081710179948,
 4.8453851048895654e-05]
In [42]:
sns.lineplot(x = [i for i in range(len(var_explained))]
,y = np.cumsum(var_explained))
plt.xlabel("Number of components used")
plt.ylabel("% Variance retrieved")
plt.show()

Since using 5 principal components retain around 97 % of variance, we'll reduce the number of dimensions from 22 to 5.

In [43]:
projection_matrix = eigen_vectors[:,0:6]
projection_matrix
Out[43]:
array([[ 0.00610584,  0.36128776, -0.10246615, -0.23763661,  0.15953517,
         0.1291187 ],
       [ 0.07996457,  0.13799931, -0.2330069 , -0.35252359, -0.31005495,
         0.16333245],
       [ 0.29752331,  0.16307742,  0.30224367, -0.0521669 , -0.03774966,
        -0.1525043 ],
       [ 0.23945232,  0.16419831,  0.36428677, -0.05029166, -0.19158467,
        -0.03781431],
       [ 0.26350611,  0.0838558 ,  0.04543437, -0.03091299,  0.26266447,
        -0.29111929],
       [-0.08947898,  0.37623948, -0.15580778,  0.28246399,  0.0416371 ,
         0.03900329],
       [ 0.32293859, -0.08754368, -0.26502924,  0.0482118 , -0.09814145,
         0.06392352],
       [ 0.22782925,  0.06109624,  0.1036229 , -0.03178625, -0.41401871,
         0.35806681],
       [ 0.28707012, -0.08775084, -0.32653607,  0.05370422,  0.14855133,
        -0.13878193],
       [-0.13197856,  0.3308902 , -0.17389288,  0.09792847, -0.1974592 ,
        -0.07817498],
       [-0.09414883,  0.32593492, -0.18610759,  0.1802854 , -0.1361438 ,
        -0.03032286],
       [ 0.30253045,  0.09344409,  0.04311069, -0.06846768, -0.023152  ,
        -0.05925697],
       [ 0.11549981,  0.23924056,  0.08276221,  0.10822575,  0.26132341,
         0.45245097],
       [ 0.14627584,  0.30128274,  0.18766408,  0.17045001,  0.12432034,
        -0.02267218],
       [ 0.01724683,  0.15501278, -0.08064119, -0.32034042,  0.37154528,
        -0.1479883 ],
       [ 0.13425249, -0.12163446,  0.06956212,  0.36589443, -0.00376275,
         0.09773203],
       [ 0.0541954 ,  0.00149225,  0.02567598, -0.2203994 ,  0.37937531,
         0.58013722],
       [ 0.29634009,  0.16329089,  0.2992249 , -0.04331185, -0.05595974,
        -0.17422561],
       [-0.09230371,  0.36775553, -0.15607898,  0.29887684, -0.00418088,
        -0.02744474],
       [-0.27804456,  0.04460718,  0.31800844, -0.06519392, -0.18828457,
         0.11185785],
       [-0.08223272,  0.20319865, -0.15356077, -0.49169821, -0.12198777,
        -0.20252877],
       [ 0.00848253, -0.01142897,  0.0371918 ,  0.11116212,  0.26697894,
        -0.13433302],
       [ 0.42116695, -0.11216908, -0.36934605,  0.06962739, -0.1337777 ,
         0.08758205]])
In [44]:
data_pca = data.dot(projection_matrix)
data_pca # Final data after dimensionality reduction
Out[44]:
0 1 2 3 4 5
0 -1.460962 -1.714735 0.703220 -0.112557 0.038267 0.097205
1 -2.314668 2.725415 -0.072621 1.269176 0.370210 0.959909
2 1.251212 -0.524874 0.211947 -0.897837 -2.097788 2.732674
3 -1.500162 -0.279262 2.233472 -0.240842 -0.035789 0.868831
4 -2.180445 -0.950593 1.029204 -1.410678 -0.814244 0.335175
... ... ... ... ... ... ...
8945 1.270828 -2.424757 -1.616353 1.650341 -2.189136 -2.198948
8946 1.048534 -2.207563 -1.741136 0.992236 -2.151763 -2.376439
8947 0.718374 -2.421604 -1.351806 1.542974 -2.037597 -2.273482
8948 -2.298085 -1.424753 0.875793 1.239225 -2.144355 -2.369188
8949 -0.127013 -0.583460 0.809681 0.825625 -3.859352 -1.813452

8950 rows × 6 columns

Now we will use the reduced data for Kmeans Clustering.

In [45]:
data[cat_features].nunique()
Out[45]:
Purchase_Type                4
PURCHASES_FREQUENCY_CLASS    4
dtype: int64
In [46]:
squared_dist = []
list_k = list(range(1, 21))
for k in list_k:
    model = KMeans(n_clusters = k,)
    model.fit(data_pca)
    squared_dist.append(model.inertia_)
# Plot squared_error against k
plt.figure(figsize=(8, 6))
plt.plot(list_k, squared_dist, '-o')
plt.xlabel('Number of clusters * k *')
plt.ylabel('Sum of squared distance')
plt.show()
In [47]:
model = KMeans(n_clusters = 4, init = 'k-means++', max_iter = 300, n_init = 10,random_state = 42)
model.fit(data_pca)
Out[47]:
KMeans(algorithm='auto', copy_x=True, init='k-means++', max_iter=300,
       n_clusters=4, n_init=10, n_jobs=None, precompute_distances='auto',
       random_state=42, tol=0.0001, verbose=0)
In [48]:
y_kmeans = model.predict(data_pca)
X = data_pca
In [51]:
plt.scatter(X[y_kmeans==0], X[y_kmeans==0], s=100, c='red', label ='Cluster 1')
plt.scatter(X[y_kmeans==1], X[y_kmeans==1], s=100, c='blue', label ='Cluster 2')
plt.scatter(X[y_kmeans==2], X[y_kmeans==2], s=100, c='green', label ='Cluster 3')
plt.scatter(X[y_kmeans==3], X[y_kmeans== 3], s=100, c='yellow', label ='Cluster 4')
# plt.scatter(X[y_kmeans==4], X[y_kmeans==4], s=100, c='yellow', label ='Cluster 5')
# plt.scatter(X[y_kmeans==5], X[y_kmeans==5], s=100, c='pink', label ='Cluster 6')
# plt.scatter(X[y_kmeans==6], X[y_kmeans==6], s=100, c='magenta', label ='Cluster 7')
plt.show()
In [50]:
pd.Series(model.labels_).value_counts()
Out[50]:
1    3923
2    3784
3     970
0     273
dtype: int64
In [52]:
cluster_data = pd.concat([data[data.columns],pd.Series(model.labels_,name='Cluster')],axis = 1)
In [53]:
cluster_data_group = cluster_data.groupby('Cluster')\
.apply(lambda x: x[data.columns].mean()).T
cluster_data_group
Out[53]:
Cluster 0 1 2 3
BALANCE 1.153541 -0.262303 -0.203554 1.530254
BALANCE_FREQUENCY 0.448630 0.198745 -0.328929 0.353106
PURCHASES 3.951053 0.123128 -0.351611 -0.238323
ONEOFF_PURCHASES 3.510723 0.015519 -0.227425 -0.163643
INSTALLMENTS_PURCHASES 2.893219 0.262507 -0.413484 -0.262929
CASH_ADVANCE -0.126190 -0.342147 -0.156587 2.030121
PURCHASES_FREQUENCY 1.110900 0.908200 -0.880831 -0.549564
ONEOFF_PURCHASES_FREQUENCY 1.827591 0.299061 -0.385711 -0.219194
PURCHASES_INSTALLMENTS_FREQUENCY 1.000859 0.824102 -0.798660 -0.499030
CASH_ADVANCE_FREQUENCY -0.303454 -0.416438 -0.017061 1.836175
CASH_ADVANCE_TRX -0.141131 -0.323221 -0.109924 1.775749
PURCHASES_TRX 3.296642 0.319998 -0.491951 -0.302877
CREDIT_LIMIT 1.633211 -0.046922 -0.300926 0.904035
PAYMENTS 2.453868 -0.115242 -0.252486 0.760411
MINIMUM_PAYMENTS 0.594186 -0.063537 -0.089233 0.437833
PRC_FULL_PAYMENT 0.521345 0.325035 -0.275880 -0.385062
TENURE 0.297725 0.071726 -0.048091 -0.186270
Monthly_avg_purchase 3.925058 0.123419 -0.352408 -0.229072
Monthly_cash_advance -0.139385 -0.341631 -0.152639 2.016346
Purchase_Type 0.326007 0.599541 2.087209 1.677320
Limit Usage 0.007490 -0.247552 0.094074 0.632089
Pay_To_Min_Pay_Ratio 0.058427 0.006855 -0.003771 -0.029461
PURCHASES_FREQUENCY_CLASS 2.890110 2.743564 0.322674 0.842268
In [54]:
fig,ax = plt.subplots(figsize=(15,10))
index = np.arange(len(cluster_data_group.columns))

cash_advance = np.log(cluster_data_group.loc['Monthly_cash_advance',:].values)
credit_score = (cluster_data_group.loc['Limit Usage',:].values)
purchase = np.log(cluster_data_group.loc['Monthly_avg_purchase',:].values)
installment = cluster_data_group.loc['INSTALLMENTS_PURCHASES',:].values
one_off = cluster_data_group.loc['ONEOFF_PURCHASES_FREQUENCY',:].values


bar_width = .10
b1 = plt.bar(index,cash_advance,color = 'r',label = 'Monthly cash advance',width = bar_width)
b2 = plt.bar(index + bar_width,credit_score,color = 'black',label = 'Credit_score',width = bar_width)
b3 = plt.bar(index + 2 * bar_width,purchase,color = 'orange',label = 'Avg purchase',width = bar_width)
b4 = plt.bar(index + 3 * bar_width,installment,color = 'b',label = 'installment',width = bar_width)
b5 = plt.bar(index + 4 * bar_width,one_off,color = 'g',label = 'One_off purchase',width = bar_width)

plt.xlabel("Clusters")
plt.title("Key Insights")
plt.xticks(index + bar_width, ('Cluster1', 'Cluster2', 'Cluster3', 'Cluster4'))
plt.legend()
plt.show()

Key Insights and Marketing Strategies:

1. Group 3 and Group 4 customers have good credit score. Thus we can give them vouchers/ extra benefits per purchases.

2. Group 2 customers have low average purchase score, while Group 1 customer have high average purchase score. Thus, we can give some reward points to group 2 customers to increase their purchase score.

3. Except Group 1, all the customers have low one_off purchases. We should work on some strategies so that customers go for one-of purchases rather than installments.